Optimal pricing with free gift cards in a two-product supply chain

We develop a model of free gift card promotions in a two-product supply chain. We analyze three cases with different gift card strategies based on whether the wholesale and retail prices are changed or unchanged. The results indicate that, in the strategy of unchanged wholesale and retail prices, the retailer and two manufacturers are better off. The gift card promotions can effectively stimulate the demands of two products. We find that the two manufacturers benefit more from the gift card promotion than the retailer does. In the strategy of unchanged wholesale prices and changed retail prices, if the gift card value is not very large, the retailer's profit margins and average consumer surplus from the gift card promotion are increasing in the gift card value. In the strategy of changed wholesale and retail prices, the retailer and two manufacturers have an incentive to raise the retail and wholesale prices under certain conditions. Furthermore, we show that, keeping the prices at the level of no gift cards is the dominant strategy for the supply chain and consumers, and the difference between retail prices and wholesale prices of two products is the key factor in determining the gift card value.